The Annals of Probability

Sufficient Statistics and Extreme Points

E. B. Dynkin

Full-text: Open access

Abstract

A convex set $M$ is called a simplex if there exists a subset $M_e$ of $M$ such that every $P \in M$ is the barycentre of one and only one probability measure $\mu$ concentrated on $M_e$. Elements of $M_e$ are called extreme points of $M$. To prove that a set of functions or measures is a simplex, usually the Choquet theorem on extreme points of convex sets in linear topological spaces is cited. We prove a simpler theorem which is more convenient for many applications. Instead of topological considerations, this theorem makes use of the concept of sufficient statistics.

Article information

Source
Ann. Probab., Volume 6, Number 5 (1978), 705-730.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995424

Digital Object Identifier
doi:10.1214/aop/1176995424

Mathematical Reviews number (MathSciNet)
MR518321

Zentralblatt MATH identifier
0403.62009

JSTOR
links.jstor.org

Subjects
Primary: 60J50: Boundary theory
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82A25 28A65

Keywords
60-02 Extreme points sufficient statistics Gibbs states ergodic decomposition of an invariant measure symmetric measures entrance and exit laws excessive measures and functions

Citation

Dynkin, E. B. Sufficient Statistics and Extreme Points. Ann. Probab. 6 (1978), no. 5, 705--730. doi:10.1214/aop/1176995424. https://projecteuclid.org/euclid.aop/1176995424


Export citation